The operator method for local fractional linear differential equations

Conformable Euler's theorem on homogeneous functions

“…Moreover, the conformable partial derivative of the order α ∈ of the real value of several variables and conformable gradient vector are defined; and a conformable version of Clairaut's theorem for partial derivatives of conformable fractional orders is proved . In short time, many studies about theory and application of the fractional differential equations are based on this new fractional derivative definition.…”

The fractional annihilator technique for solving nonhomogeneous fractional linear differential equations

“…Indeed, they employed the same methods of the ordinary case with a bit adaptation to finding the solution of the conformable fractional differential equations. Unal et al [9] and Al Horani et al [2] used the variation of parameters method and Unal et al [10] utilized the operator method for giving a particular solution of nonhomogeneous sequential linear conformable fractional differential equations. Also, these same fractional differential equations have been solved with the help of undetermined coefficient method in [5].…”

The extremal iteration solution to a coupled system of nonlinear conformable fractional differential equations

“…It should be noted that the idea of Katugampola is interesting and more general. Asawasamrit et al [3] obtained the existence of solutions for periodic boundary value problems for impulsive conformable fractional integro-differential equations.Ünal et al [15] presented the particular solution for non-homogeneous sequential linear local (conformable) fractional differential equations by the help of the operator method. In [6], Bayour et al proved the existence of solution to a conformable fractional nonlinear differential equation with initial condition using the notion of tube solution and Schauder's fixed-point theorem.…”